Michael Gove has warned senior colleagues to avoid a re-run of “project fear” during a crunch cabinet meeting over what Brexit end state the government should be aiming for, the Guardian understands.

Those present claimed the environment secretary – who was one of the figureheads of the Vote Leave campaign – urged the room to avoid a repeat of the divisive arguments of the EU referendum.

Details of the cabinet discussions emerged as Theresa May told her cabinet that she aims to pursue a bespoke trade deal that is “significantly more ambitious” than the EU’s deal with Canada, in the first formal discussion ministers have held about goals for final outcome.

That position was broadly backed by the leading ministers, who took it in turns to have their say as British negotiators gear up to enter phase two of talks, focused on transition and then the future trading arrangement.

One source said Gove, backed by Boris Johnson and others, was pushing for the government to adopt an optimistic tone about Britain’s exit from the EU, but that his comments were not directed at any colleagues in particular.

However another individual said they felt he was hitting out at the chancellor, Philip Hammond, and effectively accusing him of “peddling project fear”.

Another figure confirmed that Gove had made a “pointed comment” aimed at Hammond but said it was over a different argument in relation to the negotiation strategy, and it was also suggested that the home secretary, Amber Rudd, told off the environment secretary in response.

In what was described as a more “lively” meeting than Monday’s Brexit inner cabinet discussion, the chancellor was supported by Rudd and others in pressing for a final outcome in which the British economy remained close to that of the EU.

Amid a spectrum of views set out at length over a long session, they wanted to see the most alignment, while others – such as Johnson and Gove – pushed for Britain to be more able to diverge on standards from the EU.

The home secretary reiterated her argument that ministers must be wary about moves that could be damaging economically and harm current jobs in the UK.

The position is backed by Hammond but also others such as the welfare secretary, David Gauke, business secretary, Greg Clark, and Damian Green – effectively the deputy prime minister.

Justine Greening, the education secretary, was also supportive, although sources insisted she did not identify herself as a backer of soft or hard Brexit. However, she did make clear that business needed certainty – particularly in some sectors, such as financial services.

Meanwhile, Johnson’s arguments about protecting Britain’s ability to opt for different regulations in the future was strongly backed by Gavin Williamson, the defence secretary, with sources claiming the culture secretary, Karen Bradley, also offered her support.

However, one source insisted that there is a growing consensus – including from Hammond and Rudd – around the idea that the UK should be able to slowly diverge in certain sectors, although such a position could be resisted by the European commission.

Staying in the single market and customs union

The UK could sign up to all the EU’s rules and regulations, staying in the single market – which provides, free movement of goods, services and people – and the customs union, in which EU members agree tariffs on external states. Freedom of movement would continue and the UK would keep paying into the Brussels pot. We would continue to have unfettered access to EU trade, but the pledge to “take back control” of laws, borders and money would not have been fulfilled. This is an unlikely outcome and one that may be possible only by reversing the Brexit decision, after a second referendum or election.

The Norway model

Britain could follow Norway, which is in the single market, is subject to freedom of movement rules and pays a fee to Brussels – but is outside the customs union. That combination would tie Britain to EU regulations but allow it to sign trade deals of its own. A “Norway-minus” deal is more likely. That would see the UK leave the single market and customs union and end free movement of people. But Britain would align its rules and regulations with Brussels, hoping this would allow a greater degree of market access. The UK would still be subject to EU rules.

The Canada deal

A comprehensive trade deal like the one handed to Canada would help British traders, as it would lower or eliminate tariffs. But there would be little on offer for the UK services industry. It is a bad outcome for financial services. Such a deal would leave Britain free to diverge from EU rules and regulations but that in turn would lead to border checks and the rise of other “non-tariff barriers” to trade. It would leave Britain free to forge new trade deals with other nations. Many in Brussels see this as a likely outcome, based on Theresa May’s direction so far.

No deal

Britain leaves with no trade deal, meaning that all trade is governed by World Trade Organisation rules. Tariffs would be high, queues at the border long and the Irish border issue severe. In the short term, British aircraft might be unable to fly to some European destinations. The UK would quickly need to establish bilateral agreements to deal with the consquences, but the country would be free to take whatever future direction it wishes. It may need to deregulate to attract international business – a very different future and a lot of disruption.

Downing Street said the meeting was “good, clear and detailed”. It said ministers agreed they would not seek a deal to keep the UK in the single market, such as through membership of the European Economic Area, calling it “democratically unsustainable” because it would mean automatically adopting EU rules without a vote.

In total, 25 ministers spoke at the final cabinet meeting of the year, which lasted an hour and 25 minutes, making a range of contributions that Downing Street said were not restricted to their specific briefs. Only James Brokenshire, the Northern Ireland secretary, did not attend.

No 10 said May hoped to secure a deal that “secures the best possible trading terms with the EU, allows the UK to set rules that are right for our situation and facilitates ambitious third-country trade deals”.

Further discussions, including about plans for a transitional period after Britain leaves the EU, are expected to be held in the new year. May has been widely rumoured to be planning a speech, to follow her Lancaster House and Florence speeches over the last 12 months, setting out the next stage of the government’s Brexit plans.

No 10 said nothing had been planned yet but the government had always intended to be “transparent about the process”.

“The PM said that in developing our future economic partnership we should be creative in designing our proposal,” the prime minister’s spokesman said. “The Brexit secretary and PM were clear that the UK is seeking a bespoke deal.”

“There is no place [for financial services]. There is not a single trade agreement that is open to financial services. It doesn’t exist,” Barnier said. He said the outcome was a consequence of “the red lines that the British have chosen themselves. In leaving the single market, they lose the financial services passport.”

Asked about these objections, the spokesman said: “This is the beginning of the phase two negotiations. You would expect the commission to be setting out their position. I would imagine you will hear a lot more from them before you hear less.”

Ministers discussed the future deal for the City, among other sectors, though did not directly address Barnier’s comments, Downing Street said.

“As we have said throughout, we are confident of negotiating a good deal for financial services and, as we have always been clear, that will be in the EU’s interest as well as ours,” the spokesman said.

No 10 said the UK’s future immigration system had not come up as part of the discussions. A government source said the focus had been the economic partnership with Europe, with work on a new immigration system already well under way and the immigration bill due to published next year.

Labour’s Chuka Umunna, a leading supporter of Open Britain which campaigns to keep Britain in the single market, said it was late in the day for the cabinet to be having its first full discussion on the future relationship with Europe.

“The cabinet cannot agree among themselves about what Brexit outcome they want beyond an unrealistic ambition to have cake and eat it,” he said.